Question

On a dry surface, the breaking distance(in meters) of a Subaru Outback can be approximated by a normal distribution, where μ=41 and σ=1.01. 7) What is the shortest breaking distance of a Subaru Outback that can be in the top 12% of breaking distances? 8) What is the longest breaking distance of a Subaru Outback that can be in the bottom 15% of breaking distances?

Answer 1

To find the shortest breaking distance of a Subaru Outback in the top 12%, we can use the z-score formula and inverse normal distribution.

Step-by-step explanation:

To find the shortest breaking distance of a Subaru Outback that can be in the top 12% of breaking distances, we need to find the z-score associated with the top 12% of the normal distribution. We can use the z-score formula: z = (x - μ) / σ, where x is the breaking distance, μ is the mean, and σ is the standard deviation.

Using the inverse normal distribution table or calculator, we can find the z-score that corresponds to the top 12%, which is approximately z = 1.17.

Now, we can rearrange the z-score formula to solve for x: x = μ + z * σ. Substituting the values, we have x = 41 + 1.17 * 1.01. Calculating this, we find that the shortest breaking distance of a Subaru Outback in the top 12% is approximately 42.18 meters.